Shouldn't be a problem. I've had various servos for 20 years, they all work with every radio I've had, including new Spektrums in my case. The only issue I know of is the frame rate setting on the Spek DX3R. The default set up works, but it does have a faster rate available for digital servos only.

Oh, and if you have real old servos, especially my age or more, and not Futaba, remember to check the order of the servo wiring.

The other way around might be more of a problem. The hotter digital servos use more power, some older ESCs might struggle to provide enough power for some of the more powerful servos.